The present invention is based on a roll stand for producing flat rolled stock, in particular metal strip,                wherein the roll stand has roll stand uprights,        wherein work rolls or work rolls and backup rolls or work rolls, intermediate rolls and backup rolls are mounted in the roll stand uprights,        wherein the rolls mounted in the roll stand uprights are rotatable about a respective rotational axes,        wherein, where work rolls or work rolls and backup rolls are mounted in the roll stand uprights, the work rolls are displaceable with respect to one another in the direction of their respective rotational axes, i.e. axially, and in the case where work rolls, intermediate rolls and backup rolls are mounted in the roll stand uprights, the work rolls or the intermediate rolls are displaceable with respect to one another in the direction of their respective rotational axes, i.e. axially,        wherein the rolls that are axially displaceable with respect to one another have in each case an effective barrel length,        wherein the rolls that are axially displaceable with respect to one another have in each case a curved contour, which extends over the entire effective barrel length.        
Such a roll stand is known for example from WO 03/022 470 A1.
In known roll stands, the contour of one of the two rolls that are axially displaceable with respect to one another is formed by a first basis function, the contour of the other of the two rolls that are axially displaceable with respect to one another is formed by a second basis function. The basis functions are functions of the location seen in the direction of the respective rotational axes. They are also determined so that they complement one another in a specific relative axial position in the unloaded state of the two rolls that are axially displaceable with respect to one another and, when there is a displacement from this axial position, form a convex or concave roll gap profile, depending on the direction of displacement.
To create even rolled stock, for example a metal strip or a plate, with a defined cross-sectional profile, it is necessary to use contour-influencing measures. Examples of such measures are the use of roll bending devices, by means of which the application of rolling force to the rolled stock and the thickness distribution over the width of the rolled stock can be specifically influenced.
For influencing the cross-sectional profile, it is known to use work rolls of a bottleneck-shaped barrel contour. Examples of such shapes are known to those skilled in the art by the terms CVC (CVC is a registered trademark of SMS Siemag AG) and SmartCrown (SmartCrown is a registered trademark of the applicant). In particular, the shape of a SmartCrown contour is explained in detail in the document cited at the beginning WO 03/022 470 A1.
The bottleneck shape of the barrel contour is used not only on work rolls, but also on intermediate rolls and backup rolls. WO 2011/069756 A1 discloses for example a roll stand for producing flat rolled stock,                wherein the roll stand has work rolls, which are supported on backup rolls or intermediate rolls and backup rolls,        wherein the work rolls and/or the intermediate rolls and/or the backup rolls are arranged axially displaceably with respect to one another in the roll stand,        wherein the work rolls and the backup rolls and also—if present, the intermediate rolls have in each case an effective barrel length,        wherein each roll of at least one pair of rolls formed by a backup roll and a work roll or by a backup roll and an intermediate roll has a curved contour extending over the entire effective barrel length,        wherein the contour of the backup roll is formed by superposing a basis function with a concave or convex additional function,        wherein, in an undisplaced state, a contour of the backup roll has a complementary shape in relation to the adjacent work roll or intermediate roll according to the basis function and, when there is a displacement, forms a convex or concave differential profile, depending on the direction of displacement.        
The superposing of the basis function with the additional function serves the purpose of reducing the maximum pressures acting on the work roll and the backup roll or on the intermediate roll and the backup roll, and of thereby increasing roll service lives and avoiding roll breakages as far as possible. The additional function is a quadratic function.
WO 2007/144 162 A1 discloses a roll stand for producing flat rolled stock,                wherein the roll stand has work rolls, which are supported on backup rolls or intermediate rolls and backup rolls,        wherein the work rolls and/or the intermediate rolls have in each case an effective barrel length,        wherein the work rolls and/or the intermediate rolls have a curved contour, which extends over the entire effective barrel length and can be described by a trigonometric function,        wherein these barrel contours complement one another only in a specific relative axial position of the rolls of the pair of rolls in the unloaded state,        wherein the backup rolls have a complementary barrel contour and, in the unloaded state, there is partial or complete complementing of the barrel contours of the backup rolls and the directly adjacent work rolls or intermediate rolls.        
A similar disclosure content can be taken from WO 2007/144 161 A1.
When rolling rolled stock, it is a general endeavor that, after the rolling, the rolled stock has a predetermined profile and is still even. Unevennesses in the rolled stock can occur in particular whenever the rolled stock is relatively thin and the relative profile of the rolled stock is changed too much during the respective rolling pass, that is whenever an uneven reduction in thickness or pass reduction takes place, seen over the width of the rolled stock. Depending on the position of the unevennesses over the width, reference is made to edge, center or quarter waves. In the prior art, edge waves and center waves can be eliminated by conventional adjusting elements such as roll displacement and roll bending. In the case of quarter waves, this is considerably more difficult.
In the prior art, a specific suppression of quarter waves by means of zonal cooling is known for cold rolling mills. In the case of hot rolling, dynamic roll cooling can be used for suppressing quarter waves. This dynamic roll cooling brings about uneven cooling, seen over the width of the rolled stock, and consequently a corresponding thermal crown of the rolls. However, this way of influencing the crown is relatively limited in its effectiveness and is also slow to take effect. It is also possible to suppress quarter waves by a specific combination of displacement and bending of the work rolls. This however presupposes that there is a sufficiently great adjusting range of the roll bending. Roll bending is however usually used in the prior art primarily for allowing a response to deviations in the rolling force during the rolling of the rolled stock, in order in particular to keep the relative or absolute rolled stock profile constant and to ensure evenness.